noise constraints effecting optimal propeller designs · noise constraints effecting optimal...
TRANSCRIPT
NASA Technical Memorandum 86967
Noise Constraints Effecting Optimal Propeller Designs
Christopher J. Miller Lewis Research Center Cleveland, Ohio
and
John P. Sullivan Purdue University West Lafayette, Indiana
Prepared for the SAE General Aviation Aircraft Meeting and Exposition sponsored by the Society of Automotive Engineers Wichita, Kansas, April 16-19, 1985
https://ntrs.nasa.gov/search.jsp?R=19850011613 2020-03-19T13:12:14+00:00Z
ABSTRACT AERODYNAMIC ANALYSIS
A p r e l i m i n a r y d e s i g n t o o l f o r advanced pro- p e l l e r s has been developed combining a f a s t v o r t e x l a t t i c e aerodynamic a n a l y s i s , a f a s t sub- s o n i c p o i n t s o u r c e n o i s e a n a l y s i s , and an o p t i - m i z a t i o n scheme u s i n g a c o n j u g a t e d i r e c t i o n s method. T w i s t , chord and sweep d i s t r i b u t i o n s a r e op t imized t o s imul t aneous ly improve bo th t h e aerodynamic performance and t h e n o i s e observed a t a f i x e d r e l a t i v e p o s i t i o n .
f o r s t r a i g h t and advanced concept b l a d e s a r e p re sen ted . The t echn iques used i n c l u d e i n c r e a s - i n g t h e b l a d e number, b l ade sweep, r educ ing t h e r o t a t i o n a l speed , s h i f t i n g t h e spanwise load ing and d i a m e t e r changes . Some methods y i e l d i m - provement i n bo th e f f i c i e n c y and n o i s e .
~
The op t ima l no ise /per formance t r a d e - o f f s
INTKODUCTIOh
PREVIOUS WORK (1,2)* HAS IDENTIFIED THE pe r - formance g a i n s and n o i s e r e d u c t i o n s a v a i l a b l e through t h e u s e o f advanced concept p r o p e l l e r b l a d e s . These works opt imized t h e per formance o n l y ; n o i s e w a s cons ide red as a s e p a r a t e i s s u e . To p r o p e r l y i n v e s t i g a t e advanced p r o p e l l e r con- c e p t s a s w e l l a s conven t iona l geomet r i e s , a d e s i g n t o o l should be a b l e t o op t imize bo th p e r - formance and n o i s e a t t h e same t ime. Th i s pape r d e s c r i b e s t h e development o f such a d e s i g n t o o l and t h e no i se /pe r fo rmance t r a d e - o f f s a v a i l a b l e from o p t i m a l geomet r i e s .
(1) a v o r t e x l a t t i c e method f o r t h e aerodynamic per formance p r e d i c t i o n ; ( 2 ) a subson ic compact s o u r c e model i n t h e t ime domain f o r t h e n o i s e p r e d i c t i o n ; and ( 3 ) an o p t i m i z a t i o n scheme us ing a c o n j u g a t e d i r e c t i o n s method.
I h e d e s i g n program c o n s i s t s o f t h r e e p a r t s :
qiuunibers i n p a r e n t h e s e s d e s i g n a t e r e f e r e n c e s a t end o f paper .
The v o r t e x l a t t i c e method has been used by v a r i o u s r e s e a r c h e r s ( 2 t o 7) i n t h e s t u d y of p r o p e l l e r per formance . The b a s i c c a l c u l a t i o n geometry i s shown i n F ig . 1. There i s a s i n g l e curved l i f t i n g l i n e d i v i d e d spanwise i n t o a s e t o f ho r seshoe v o r t i c e s . Th i s l i f t i n g l i n e i s a long t h e qua r t e r - chord l i n e of t h e b l ade . A t c o n t r o l p o i n t s on t h e t h r e e - q u a r t e r chord l i n e , a boundary c o n d i t i o n of no f low th rough t h e mean camber s u r f a c e i s imposed. The t r a i l i n g vor- t i c e s r e p r e s e n t i n g t h e wake a r e p r e s c r i b e d t o l i e on t h e s u r f a c e swept o u t by t h e q u a r t e r - chord l i n e w i t h p i t c h d e f i n e d by t h e advance r a t i o . Th i s method i s a s t e a d y symmetric a n a l - y s i s , s o t h e r a d i a l c i r c u l a t i o n d i s t r i b u t i o n i s t h e same f o r a l l b l a d e s .
The e q u a t i o n s t o be so lved a r e based on t h e boundary c o n d i t i o n t h a t t h e r e i s no f low th rough t h e chord p l a n e s u r f a c e a t t h e c o n t r o l p o i n t s . The boundary c o n d i t i o n f o r t h e j t h v o r t e x l a t t i c e e lement i s t h e r e f o r e :
V . * f ; . = .vinflow, + r. xu + v . ;i. = o 3
< ’ J r J J
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,L s h a f t speed and a x i s [ r a d i a n s / s e c )
2 V . t o t a l induced v e l o c i t y a t 2:.
J J
1
The B i o t - S a v a r t Law i s u s e d t o c a l c u l a t e t h e i n d u c e d v e l o c i t i e s d u e t o t h e h o r s e s h o e v o r - t i c i e s . The i n d u c e d v e l o c i t y a t t h e c o n t r o l p o i n t o f l a t t i c e e l e m e n t j o f b l a d e 1 d u e t o t h e v o r t e x o f e l e m e n t i o f b l a d e k i s g i v e n b y i
w h e r e
r . c i r c u l a t i o n s t r e n g t h o f h o r s e s h o e v o r t e x i p e r u n i t l e n g t h
K t i p p r o p e l l e r t i p r a d i u s
d h i k 2
d i f f e r e n t i a l segment o f t h e h o r s e s h o e v o r t e x .
S i n c e t h e c i r c u l a t i o n s a re t h e unknowns , t h e b o u n d a r y c o n d i t i o n p r o v i d e s a se t o f s i m u l t a n - e o u s e q u a t i o n s f o r t h e c i r c u l a t i o n s .
t h e f o r c e s on e a c h e l e m e n t a r e c a l c u l a t e d u s i n g t h e K u t t a - J o u k o w s k i l a w . T h e s e f o r c e s a r e summed t o p r o v i d e t h e o v e r a l l f o r c e s on t h e p r o p e l l e r . The b l a d e f o r c e s f o r t h e j t h e l e m e n t a r e g i v e n b y :
Once t h e c i r c u l a t i o n s h a v e b e e n d e t e r m i n e d ,
cd o z e r o l i f t d r a g c o e f f i c i e n t
C c h o r d l e n g t h
K d r a g p o l a r c o n s t a n t .
A s a v e r i f i c a t i o n , F i g s . 2 t o 5 compare t h e p r e d i c t e d r e s u l t s w i t h e x p e r i m e n t a l t e s t d a t a . The d a t a i n b i g s . 2 and 3 a r e f o r a r e p r e s e n t a - t i v e g e n e r a l a v i a t i o n p r o p e l l e r t e s t e d a t t h e hASA Lewis k e s e a r c h L e n t e r ( A ) . F i g s . 4 and 5 , t a k e n f rom R e f . (?), a r e f o r a q u a r t e r s c a l e g e n e r a l a v i a t i o n p r o p e l l e r modeled a f t e r t h e b l a d e on a C e s s n a 1 7 2 : t h e PlcCauley lL160. I n b o t h c a s e s , t h e p r e d i c t e d p e r f o r m a n c e a g r e e s w e l l , b u t t h e p r e d i c t e d v a r i a t i o n o f power c o e f f i c i e n t ( w i t h a d v a n c e r a t i o ( J )
r e s u l t s . The f i x e d wake model i s p a r t i a l l y t o b lame: t h e i n d u c e d v e l o c i t i e s would i n c r e a s e t h e wake h e l i x a n g l e , and h e n c e would i n c r e a s e t h e i n d u c e d d r a g a t t h e h i g h e r l o a d i n g s . T h i s f a c t o r would r a i se t h e h i g h l o a d i n g p r e d i c t i o n of Cp and s t r a i g h t e n t h e c u r v e .
I n t h e s e f i g u r e s , t h e f o l l o w i n g s y m b o l s a r e u s e d
n b l a d e number
The d a t a i n
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A
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' p o i n t
Dv v i s c o u s d r a g e s t i m a t e .
Here t h e v i s c o u s d r a g i s c a l c u l a t e d b a s e d on t h e s e c t i o n l i f t c o e f f i c i e n t o f t h e e l e m e n t , L, :
= 1 s c (VM * VM, D v 2 Po J J
(5)
V a x i a l i n f l o w v e l o c i t y ( f l i g h t v e l o c i t y )
A V/iik = J / n = a l t e r n a t e a d v a n c e r a t i o
C T T/ (p0n2D4) = t h r u s t c o e i f i c i e n t
~p p/(p,n3~5) = power c o e f f i c i e n t .
hOISE ANALYSIS
The n o i s e a n a l y s i s method i s b a s e d on t h e work o f Lowson (lo). t h a t t h e r e i s n o mean f l o w ( s t a t i c o p e r a t i o n ) and t h a t t h e c o n t i n u o u s d i s t r i b u t i o n o f n o i s e s o u r c e s o n t h e b i a d e c a n be r e p r e s e n t e d by p o i n t s o u r c e s . T h e s e a s s u m p t i o n s a r e m e t when c o n s i d - e r i n g low s p e e d o p e r a t i o n , a s i n t a k e - o f f and c l i m b , s u c h t h a t t h e h e l i c a l t i p s p e e d s a r e l e s s t h a n a b o u t Plach 0.75.
Lowson d i d n o t c o n s i d e r t h e n o i s e p r o d u c e d by a r a d i a l f o r c e i n h i s a n a l y s i s . S o , a n a d d i - t i o n a l t e r m f o r t h e r a d i a l f o r c e n o i s e h a s b e e n d e r i v e d f o r u s e i n t h i s s t u d y . The e q u a t i o n w h i c h must be s o l v e d f o r t h e n o r m a l i z e d p r e s s u r e p e r t u r b a t i o n p r o d u c e d by t h e p r o p e l l e r i s :
T h i s a n a l y s i s a s s u m e s
where
'd v i s c o u s d r a g c o e f f i c i e n t
2
2
9 a n g l e f rom R a x i s .
.[XT j - ( X r M r - xs) (k? ++)I
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s p e e d o f sound
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i iRs/ao
I Iri l I = I I x i - y i l I
( x ,Y ,o ) = ( r o b s c o s ( $ ) , r o b s s i n ( $ ) , 0) = o b s e r v e r p o s i t i o n
( X s , R s c o s ( e ) , Rs s i n ( e ) ) = s o u r c e p o s i t i o n
f o r c e c o e f f i c i e n t s o n a n e l e m e n t
mass f l u x as f o r c e t e r m = aoqm/ p . n 2 ~ 4
volume f l u x
s h a f t s p e e d [ r p s / s ]
p r o p e l l e r d i a m e t e r
s p e c i f i c h e a t r a t i o = 1 . 4
a z i m u t h a l a n g l e
F o r t h e n o i s e a n a l y s i s , t h e x - a x i s i s t h e f o r - ward a x i s of r o t a t i o n (ii). T h i s e q u a t i o n i s e v a l u a t e d a t t h e n o r m a l i z e d r e t a r d e d t i m e 6 , f o r t h e o b s e r v e r t i m e d e t e r m i n e d b y :
w h e r e
A B S sweep i n t r o d u c e d d e l a y .
The p r o p e l l e r i s modeled a s a d i s t r i b u t i o n o f p o i n t n o i s e s o u r c e s w i t h s t r e n g t h s p r o p o r - t i o n a l t o t h e l o c a l l o a d i n g a n d t h i c k n e s s . Each o f t h e v o r t e x l a t t i c e e l e m e n t s i s modeled as two n o i s e e l e m e n t s i n t h e s p a n w i s e d i r e c t i o n ( o r a l o n g t h e h u b t o hub q u a r t e r - c h o r d l i n e f o r t h e b i - b l a d e ) t o improve t h e a s s u m p t i o n o f compact - n e s s . The l a y o u t o f n o i s e s o u r c e s i s shown i n F i g . 6.
The f o r c e c o e f f i c i e n t s , (ACT,AC~,ACR), o n t h e n o i s e e l e m e n t s a r e h a l f o f t h e c o e f f i c i e n t o n t h e p a r e n t a e r o d y n a m i c e l e m e n t , a n d t h e t h i c k n e s s s o u r c e t e r m i s w r i t t e n i n t h e f o r m o f a f o r c e c o e f f i c i e n t ( A K ~ ) f o r c a l c u l a t i o n e a s e . The s t r e n g t h a n d p o s i t i o n s o f t h e s o u r c e - s i n k p a i r u s e d t o r e p r e s e n t t h i c k n e s s a re c h o s e n s o t h a t t h e K a n k i n e body p r o d u c e d h a s t h e same c h o r d a s t h e l o c a l b l a d e s e c t i o n , a n d t h e same f r o n t a l area a s t h e n o i s e e l e m e n t .
s u r e p e r t u r b a t i o n (Eq. ( 6 ) ) i s c a l c u l a t e d a t e q u a l l y s p a c e d p o i n t s i n r e t a r d e d t i m e , e , a l o n g w i t h t h e a s s o c i a t e d o b s e r v e r t imes , t . T h e s e p r e s s u r e s a r e t h e n i n t e r p o l a t e d t o a n e q u a l l y s p a c e d s e t i n o b s e r v e r t i m e . The a d v a n t a g e o f t h i s m e t h o d , d u e t o l l u n r o (G), i s t h a t t h e t i m e consuming s d l u t i o n f o r t h e r e t a r d e d t i m e a s s o c i - a t e d w i t h a g i v e n o b s e r v e r t i m e i s e l i m i n a t e d . A l s o , t h e d i s t r i b u t i o n o f p o i n t s i n o b s e r v e r t i m e i s d e n s e s t i n t h e r e g i o n o f t h e p r e s s u r e p e a k s w h i s h r e s u l t s i n a n a c c u r a t e i n t e r p o l a t i o n o f t h e p e a k s . The m u l t i p l e b l a d e waveform i s c r e a t e d f r o m t h i s s i n g l e b l a d e waveform by s u p e r p o s i t i o n w i t h t h e p r o p e r p h a s e d e l a y s .
h a s b e e n p r o d u c e d , a F a s t F o u r i e r T r a n s f o r m i s u s e d t o o b t a i n t h e h a r m o n i c m a g n i t u d e s . The o v e r a l l sound p r e s s u r e l e v e l (OASPL) n o i s e meas- u r e i s t h e n c a l c u l a t e d f r o m t h e s e h a r m o n i c s b o t h i n dB and u s i n g t h e A-weighted s c a l e f o r dBA.
u r e d n e a r f i e l d n o i s e , o n e t i p r a d i u s away i n t h e p l a n e of r o t a t i o n f o r t h e q u a r t e r s c a l e p r o p e l l e r t e s t d a t a i n R e f s . (2) a n d (12) t o (lit). a i c t i o n and t h e e x p e r i m e n t a l d a t a , b u t t h e wave- f o r m s h a p e and m a g n i t u d e a r e i n e x c e l l e n t a g r e e - ment . A d d i t i o n a l d a t a i s a v a i l a b l e b o t h a h e a d o f a n d b e h i n d t h e p l a n e o f r o t a t i o n . T h e s e d a t a a r e compared w i t h p r e d i c t i o n s i n R e f . (E). The c o m p a r i s o n s show t h e same p h a s e s h i f t a l o n g w i t h a sma l l m a g n i t u d e d i f f e r e n c e . T h i s m a g n i t u d e
To i n c r e a s e t h e e x e c u t i o n s p e e d , t h e p r e s -
Once t h e p e r t u r b a t i o n p r e s s u r e t i m e h i s t o r y
F i g u r e 7 c o m p a r e s t h e p r e d i c t e d and meas-
T h e r e i s a p h a s e s h i f t b e t w e e n t h e p r e -
3
d i f f e r e n c e r e s u l t s i n a few t e n t h s o f a dB d i f - f e r e n c e i n t h e OASPL.
r ( i ) b 1 a d e e 1 e m e 11 t c i r c u 1 a t i o n s
OPTIMIZATION MCTHOD
An o p t i m i z a t i o n method a u t o m a t e s t h e p r o c - e s s of c h o o s i n g v a l u e s o f t h e i n d e p e n d e n t v a r i - a b l e s t o c r e a t e a " b e s t " r e s u l t . I n t h i s work , t h e i n d e p e n d e n t v a r i a b l e s a r e t h e t w i s t , c h o r d , a n d sweep d i s t r i b u t i o n s , w h i l e t h e m e a s u r e o f t h e r e s u l t i s c a l l e d t h e I n d e x o f P e r f o r m a n c e . The I n d e x o f P e r f o r m a n c e (IP) c o n t a i n s b o t h t h e a e r o d y n a m i c p e r f o r m a n c e and n o i s e o f t h e p r o - p e l l e r and i s f o r m u l a t e d s o t h a t a n optimum g e o m e t r y c o r r e s p o n d s t o a minimum o f t h e f u n c - t i o n . D i f f e r e n t o p t i m a l g e o n L e t r i e s a r e o b t a i n e d by c h a n g i n g t h e r e l a t i v e i m p o r t a n c e o f n o i s e v e r s u s e f f i c i e n c y i n t h e I P .
The c o n j u g a t e d i r e c t i o n s method u s e d f o r t h e o p t i m i z a t i o n i s t h a t o f P o w e l l (16) a s modi- f i e d by L a n g w i l l (E). A f t e r s e a r c h i n g a l o n g e a c h of t h e c u r r e n t s e t o f s e a r c h d i r e c t i o n s , t h e t e c h n i q u e s e a r c h e s a l o n g t h e d i r e c t i o n re- s u l t i n g f r o m t h e end p o i n t s o f t h e i n t e r m e d i a t e s t e p s . T h i s c o m p o s i t e d i r e c t i o n i s t h e c a n d i - d a t e c o n j u g a t e d i r e c t i o n . I f t h e s e a r c h p r o v e s r r u i t f u l , t h e c o n j u g a t e d i r e c t i o n r e p l a c e s o n e o f t h e p r e v i o u s s e a r c h d i r e c t i o n s .
r a t i c f i t t o t h r e e f u n c t i o n e v a l u a t i o n s . I f t h e e s t i m a t e d minimum l i e s o u t s i d e t h e f i t i n t e r v a l , t h e i n t e r v a l i s s h i f t e d t o w a r d s t h e minimum u n t i l t h e minimum i s b r a c k e t e d . Then , i f t h e p r e d i c t i o n f o r t h e v a l u e o f t h e o b j e c t i v e f u n c - t i o n d o e s n o t a g r e e w i t h t h e computed v a l u e , t h e f i t i n t e r v a l w i d t h may b e r e d u c e d . The minimum i n t e r v a l w i d t h a l l o w a b l e i s b a s e d on t h e r e l a - t i v e m a g n i t u d e o f t h e random p o r t i o n o f t h e o b j e c t i v e f u n c t i o n . T h i s method i s r a p i d and p r o v i d e s some immuni ty t o n u m e r i c a l n o i s e i n t h e o b j e c t i v e f u n c t i o n .
The I n d e x o f P e r f o r m a n c e ( 1 P ) i n c o r p o r a t e s t h e c o n s t r a i n t s i n t h e manner o f t h e SUMT f o m - i l l a t i o n d e v e l o p e d by F i a c c o and PlcCormick (2) :
The l i n e s e a r c h e s are d o n e u s i n g a quad-
where
LT p r o p e l l e r t h r u s t c o e f f i c i e n t
( P p r o p e l l e r power c o e f f i c i e n t
($"'get p a r a m e t e r t o o b t a i n t h e d e s i r e d Cp
I\ OASPL n o i s e m e a s u r e i n (dU) o r (CiBA)
m limit l i m i t v a l u e o f t o t a l sweep
a t h e r e l a t i v e i v p o r t a n c e o f e f f i c i e n c y v e r s u s n o i s e
b n o r m a l i z a t i o n f o r n o i s e
n e l s number o f b l a d e e l e m e n t s
Wc Cp w e i g h t i n g
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12' w e i g h t on sweep " k i n k " c o n s t r a i n t
WS L w e i g h t to f o r c e h i - b l a d e s y m m e t r i c l o a d i n g .
l h e m e a s u r e o f sweep, S', i s g i v e n by
a n d t h e m e a s u r e o f i n t e r - e l e m e n t a n g l e i s
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xh' 1 , Y l i th node p o i n t c o o r d i n a t e s
t a n g e n t to t h e bound segment b e t w e e n n o d e s j and j + 1.
?!
B e c a u s e o f t h e n u m e r i c a l n o i s e p r e s e n t i n t h e c a l c u l a t i o n , t h e w e i g h t i n g s i n (8) a r e n o t d e c r e a s e d t o z e r o a s would be c u s t o m a r y . I n - s t e a d , t h e w e i g h t i n g s a r e h e l d c o n s t a n t and t h e o f f s e t t a r g e t v a l u e s a r e a d j u s t e d . T h i s p r e - v e n t s t h e a i n p l i f i c a t i o n o f t h e random n o i s e i n t h e IP.
To f u r t h e r s p e e d t h e o p t i m i z a t i o n , t h e scheme i s c l o s e l y c o u p l e d w i t h t h e a e r o d y n a m i c a n a l y s i s r o u t i n e . T h i s i s d o n e by r e c a l c u l a t i n g o n l y t h o s e p o r t i o n s o f t h e model a f f e c t e d by g e o m e t r y c h a n g e s . F o r e x a m p l e , i f a n e l e m e n t i s r e t w i s t e d , o n l y t h e i n d u c e d v e l o c i t i e s a t t h e c o n t r o l p o i n t c h a n g e . The i n d u c e d v e l o c i t i e s a t t h e bound segment and a l l i n d u c e d v e l o c i t i e s on t h e o t h e r e l e m e n t s r e m a i n t h e same and a r e re- u s e d to c a l c u l a t e t h e p e r f o r m a n c e . T h i s i s most b e n e f i c i a l i n i t i a l l y when t h e s e a r c h d i r e c t i o n s c o r r e s p o n d t o s i n g l e g e o m e t r i c q u a n t i t i e s . Com- p a r e d w i t h a c o m p l e t e s o l u t i o n f o r a d e s i g n s t a t e , t h i s t e c h n i q u e i s 2 t o 24 t imes f a s t e r f o r e v a l u a t i o n s of a 1 2 e l e m e n t b l a d e m o d e l .
method was t o maximize s t r a i g h t b l a d e i d e a l An i n i t i a l t e s t c a s e f o r t h e o p t i m i z a t i o n
4
e f f i c i e n c y a s a f u n c t i o n o f t h e t w i s t d i s t r i b u - t i o n . G o l d s t e i n ' s c i r c u l a t i o n d i s t r i b u t i o n (g), w h i c h y i e l d s t h e maximum i d e a l e f f i c i e n c y u n d e r t h e s e a s s u m p t i o n s , was o b t a i n e d , v e r i f y i n g t h e method.
F o r a more r e a l i s t i c p r e d i c t i o n , a v i s c o u s d r a g e s t i m a t e i s i n c l u d e d . T h i s e s t ima te a s s u m e s a l a m i n a r f l o w s e c t i o n o p e r a t i n g i n t h e l a m i n a r b u c k e t w i t h t h e same d e p e n d e n c e o f c d o on s e c t i o n t h i c k n e s s a s f o r a Clark-Y a i r f o i l ( t o b e c o n s e r v a t i v e ) . The C i f o r s t a l l was c h o s e n t o h e 1 . 2 , a n d s t a l l was modeled b y a s h a r p i n c r e a s e i n t h e s e c t i o n d r a g c o e f f i c i e n t . T h i s d r a g model i s j u s t i f i e d b e c a u s e g i v e n t h e d e s i g n l i f t c o e f f i c i e n t , t h e c o r r e s p o n d i n g a i r - f o i l s h a p e c a n h e f o u n d . By i n c l u d i n g v i s c o u s e f f e c t s , t h e c h o r d d i s t r i b u t i o n c a n h e a d e s i g n v a r i a b l e i n a d d i t i o n t o t h e t w i s t d i s t r i b u t i o n .
To i n v e s t i g a t e t h e t r a d e - o f f s i n v o l v e d when n o i s e i s c o n s i d e r e d , v a r i o u s t e c h n i q u e s f o r n o i s e r e d u c t i o n a r e a p p l i e d t o a s t r a i g h t , a p r o p l e t e d a n d a h i - b l a d e d p r o p e l l e r . T h e s e t e c h n i q u e s i n c l u d e : r e d u c i n g t h e d i a m e t e r t o r e d u c e t i p s p e e d , s h i f t i n g t h e l o a d i n g i n b o a r d , a n d r e d u c - i n g t h e r o t a t i o n a l r a t e t o r e d u c e t i p s p e e d . F o r t h e s e t r a d e - o f f s , t h e d e s i g n v a r i a b l e s a r e t h e t w i s t , c h o r d and sweep d i s t r i b u t i o n s .
N o i s e r e d u c t i o n s a r e a c h i e v e d t h r o u g h two m e c h a n i s m s : p h a s e c a n c e l l a t i o n and n o i s e s o u r c e s t r e n g t h r e d u c t i o n . P h a s e c a n c e l l a t i o n i s a c c o m p l i s h e d e i t h e r by a d d i n g b l a d e s or t h r o u g h sweep. The s o u r c e s t r e n g t h d e p e n d e n c e o n p r o - p e l l e r p a r a m e t e r s d e p e n d s o n t h e t y p e o f n o i s e s o u r c e . The p r e s s u r e p e r t u r b a t i o n s d u e t o t h i c k n e s s t e r m s a re p r o p o r t i o n a l t o r e l a t i v e Mach number s q u a r e d , a n d t h e p e r t u r b a t i o n s d u e t o f o r c e t e r m s a r e p r o p o r t i o n a l t o Mach number c u b e d . L o a d i n g n o i s e i s l i n e a r l y p r o p o r t i o n a l t o t h e b l a d e l o a d i n g s t h o u g h . Hence , r e d u c i n g t h e r e l a t i v e Mach number t h r o u g h a r e d u c t i o n o f t h e r o t a t i o n a l s p e e d or a r e d u c t i o n o f t h e p r o - p e l l e r d i a m e t e r a r e e x p e c t e d t o h a v e a l a r g e e f f e c t on t h e n o i s e .
i n F i g s . 8 t o 1 0 f o r t h e t h r e e b l a d e t y p e s . The n o i s e i s c a l c u l a t e d a t a f i x e d p o s i t i o n , 333 t i p r a d i i away, and 30" b e h i n d t h e p l a n e o f r o t a - t i o n . T h i s a n g l e i s n e a r t h e maximum o f t h e d i r e c t i v i t y p a t t e r n , and a t a d i s t a n c e a p p r o p r i - a t e f o r s i d e l i n e m e a s u r e m e n t s i n t a k e - o f t . The t r a d e - o f f c u r v e s were o b t a i n e d by v a r y i n g t h e p a r a m e t e r s i n t h e I P , Lq. (8). The w e i g h t i n g v a l u e , a , was s h i f t e d f rom c o n s i d e r a t i o n o f o n l y a e r o d y n a m i c p e r f o r m a n c e t o w a r d s c o n s i d e r a - t i o n o f n o i s e o n l y . Eor e a c h v a l u e o f t h e w e i g h t i n g p a r a m e t e r , t h e p r o p e l l e r g e o m e t r y was r e - o p t i m i z e d . T h e s e o p t i m a l g e o m e t r i e s p r o d u c e t h e c u r v e s shown.
t h e s t r a i g h t b l a d e . A s i m p l e a n d v e r y e f f e c t i v e t e c h n i q u e f o r p e r f o r m a n c e improvement i s t o i n c r e a s e t h e b l a d e number. The b l a d e number a s shown s t a r t s a t t h r e e and i n c r e a s e s i n i n c r e - m e n t s o f o n e . When e i t h e r ttle p r o p e l l e r s o l i d - i t y i s h e l d c o n s t a n t , o r t h e b l a d e p l a n f o r m i s h e l d c o n s t a n t , t h e n o i s e i s d e c r e a s e d w h i l e t h e e f f i c i e n c y g o e s up . A d d i t i o n a l b l a d e s r e d u c e
The r e s u l t i n g o p t i m i z e d t r a d e - o f f s a r e shown
F i g u r e 8 shows t h e t r a d e - o f f r e s u l t s f o r
t h e n o i s e by i n t r o d u c i n g p h a s e c a n c e l l a t i o n f o r c e r t a i n h a r m o n i c s w h i l e t h e s t r e n g t h s o f t h e r e m a i n i n g h a r m o n i c s a r e c o n s t a n t . The e f f i - c i e n c y i s i n c r e a s e d b e c a u s e of r e d u c e d t i p a n d s w i r l l o s s e s . The c o n s t a n t s o l i d i t y c a s e s h a v e h i g h e r e f f i c i e n c i e s t h a n t h e c o n s t a n t p l a n f o r m c a s e s b e c a u s e t h e v i s c o u s d r q i s l o w e r .
t i v e method shown. T h i s t r a d e - o f f s t a r t s w i t h n o sweep, and e n d s u p w i t h t h e t i p swept h a c k a b o u t 45" f rom t h e i n i t i a l g e o m e t r y . The p o i n t s a l o n g t h e c u r v e r e p r e s e n t e q u a l i n c r e m e n t s i n t h e w e i g h t i n g s , b u t u n e q u a l c h a n g e s i n sweep. Sweep r e d u c e s t h e n o i s e by i n t r o d u c i n g a p h a s e s h i f t a n d s u b s e q u e n t p h a s e c a n c e l l a t i o n b e t w e e n n o i s e f r o m d i f f e r e n t s e c t i o n s o f t h e b l a d e . I f t h e s w e p t b l a d e i s c o n c u r r e n t l y r e t w i s t e d t o m a i n t a i n t h e r a d i a l l o a d d i s t r i b u t i o n , t h e e f f i - c i e n c y w i l l r e m a i n n e a r l y t h e s a m e . A drawback t o sweep i s t h a t f o r a b l a d e w i t h a low r o t a - t i o n a l Mach number , t h e amount of sweep n e e d e d f o r a u s e f u l r e d u c t i o n i n n o i s e i s l a r g e .
R e d u c i n g t h e r o t a t i o n a l s p e e d c a n r e d u c e t h e n o i s e w i t h a s m a l l e f f i c i e n c y p e n a l t y . The c h a n g e s shown c o r r e s p o n d t o 5 p e r c e n t c h a n g e s i n r o t a t i o n a l s p e e d . The h i g h e r a d v a n c e r a t i o r e s u l t s i n h i g h e r b l a d e l o a d i n g s , h e n c e g r e a t e r t i p a n d s w i r l l o s s e s , b u t t h e r e i s a l a r g e d e c r e a s e i n t h e n o i s e p r o d u c e d .
t h e n o i s e , b u t w i t h a s i z e a b l e e f f i c i e n c y pen- a l t y . The e f f i c i e n c y d r o p s b e c a u s e t h e e f f e c - t i v e d i a m e t e r i s r e d u c e d , i n c r e a s i n g t h e d i s k l o a d i n g . The i n b o a r d s h i f t of t h e l o a d i n g r e d u c e s t h e n o i s e by r e d u c i n g t h e s t r e n g t h o f t h e h i g h Mach number s o u r c e s , and i n c r e a s i n g t h e s t r e n g t h of t h e low Mach number s o u r c e s . A l t h o u g h h a r d t o q u a n t i f y , t h e l o a d i n g s shown a r e s h i f t e d so t h a t t h e p e a k moves f rom t h e 75 p e r c e n t r a d i u s i n b o a r d t o a b o u t t h e 60 p e r c e n t r a d i u s .
A v e r y i n e f f e c t i v e method f o r r e d u c i n g t h e n o i s e i s shown t o be r e d u c i n g t h e d i a m e t e r . Changes h e r e c o r r e s p o n d t o 5 p e r c e n t r e d u c t i o n s i n d i a m e t e r . The n o i s e i s r e d u c e d by t h e r e m o v a l o f t h e h i g h Mach number t i p s o u r c e s . The r e m a i n i n g s o u r c e s a r e i n c r e a s e d i n s t r e n g t h t h o u g h , w h i c h o f f s e t s some o f t h e r e d u c t i o n s . The e t f i c i e n c y d r o p s s h a r p l y b e c a u s e o f t h e i n c r e a s e d d i s k l o a d i n g . T h i s p e r t o r m a n c e pen- a l t y i s l a r g e a n d makes t h e method u n d e s i r a b l e .
F i g u r e 9 shows t h e t r a d e - o f f r e s u l t s f o r a p r o p l e t e d b l a d e . The c h a r a c t e r o f some o f t h e t r a d e - o f f c u r v e s h a s c h a n g e d f rom t h e s t r a i g h t b l a d e r e s u l t s . Most n o t a b l e i s t h e b l a d e number t r a d e - o f f w h i c h n o l o n g e r shows a n i n c r e a s e i n e f f i c i e n c y w i t h t h e d e c r e a s e i n n o i s e . T h i s c u r v e i s f o r a c o n s t a n t p l a n f o r m ; f o r s t r u c t u r a l r e a s o n s , t h e t i p t h i c k n e s s and c h o r d a r e f i x e d . W i t h i n c r e a s i n g b l a d e number , t h e c o n s t a n t b l a d e p l a n f o r m p r o p e l l e r h a s i n c r e a s e d v i s c o u s d r a g . S i n c e t h e t i p d e v i c e i s most b e n e f i c i a l a t h i g h e r b l a d e l o a d i n g s , i n c r e a s i n g t h e b l a d e number w i l l a l s o r e d u c e t h e e f f i c i e n c y g a i n . T h i s r e d u c e d e f f i c i e n c y g a i n , a l o n g w i t h t h e v i s c o u s d r a g i n c r e a s e , combine t o r e d u c e t h e e f f i c i e n c y o f a p r o p l e t e d p r o p e l l e r . F u r t h e r ,
Sweeping t h e b l a d e i s t h e n e x t most e f f e c -
S h i f t i n g t h e l o a d i n g i n b o a r d c a n r e d u c e
5
w h i l e t h e t o t a l l o a d i n g r e m a i n s a p p r o x i m a t e l y c o n s t a n t , t h e a d d i t i o n a l t i p t h i c k n e s s n o i s e o f f s e t s t h e n o i s e r e d u c t i o n s f rom i n c r e a s e d b l a d e number.
u n t a v o r a b l e t r e n d s s i m i l a r t o t h o s e f o r t h e s t r a i g h t b l a d e . L o a d i n g s h i f t p e n a l i z e s a p r o - p l e t r d p r o p e l l e r inure by u n l o a d i n g t h e t i p and p r o p l e t , w h i l e t h e p r o p l e t ' s e f f e c t a t h ig l i l o a d i n g s b e n e f i t s t h e d i a m e t e r r e d u c t i o n c a s e s .
a b l e for t h e p r o p l e t e d p r o p e l l e r t h a n t h e s t r a i g h t b l a d e p r o p e l l e r . As t h e r o t a t i o n a l s p e e d i s r e d u c e d t o d e c r e a s e t h e n o i s e , t h e l o a d i n g i n c r e a s e s . S i n c e p r o p l e t s p e r f o r m b e t - t e r a t t h e h i g h e r l o a d i n g s , t h e r e i s l e s s e f f i - c i e n c y l o s s .
b l a d e p r o p e l l e r . A g a i n , t h e l o a d i n g s h i f t and d i a m e t e r r e d u c t i o n methods h a v e u n f a v o r a b l e t r e n d s . B l a d e number i n c r e a s e s a r e f o r a f i x e d p l a n f o r m , t o s u p p o r t t h e t i p d e v i c e , and s o i n c r e a s e t h e v i s c o u s d r a g w h i l e d e c r e a s i n g t h e e f f e c t i v e n e s s of t h e t i p d e v i c e . R o t a t i o n a l s p e e d r e d u c t i o n i s more f a v o r a b l e t h a n f o r e i t h e r t h e s t r a i g h t b l a d e or p r o p l e t e d p r o p e l - l e r . T h i s i s a r e s u l t of t h e more e f f e c t i v e t i p d e v i c e r e t a i n i n g more o f t h e e f f i c i e n c y as t h e l o a d i n g i n c r e a s e s . U s i n g a r o t a t i o n a l s p e e d r e d u c t i o n , t h e t h r e e way b i - b l a d e p r o p e l l e r h a s a b o u t 1 dBA l e s s n o i s e a t t h e same e f f i c i e n c y a s t h e s i x way c o n s t a n t p l a n f o r m s t r a i g h t b l a d e p r o p e l l e r .
T h e m o s t i n t e r e s t i n g c u r v e i s f o r t h e e f f r c t o f sweep on a b i - b l a d e p r o p e l l e r . A f t e r a i l i n i t i a l d e c r e a s e i n e f f i c i e n c y w i t h d e c r e a s - i n g n o i s e , t h e t r e n d f l a t t e n s . I f t h e c u r v e i s e x t r a p o l a t e d t o t h e e f f i c i e n c y of a th ree-way c o n s t a n t p l a n f o r m s t r a i g h t b l a d e p r o p e l l e r , t h e Lliree-way b i - b l a d e p r o p e l l e r would h a v e a n o i s e l e v e l t h a t i s 1 4 dBA l o w e r t h a n for t h e s t r a i g h t b l a d e p r o p e l l e r .
s UI'PlAKi
L o a d i n g s h i f t and d i a m e t e r r e d u c t i o n show
R o t a t i o n a l s p e e d r e d u c t i o n i s more f a v o r -
F i g u r e 10 p r e s e n t s t h e t r a d e - o f f s f o r a b i -
A u n i q u e p r e l i m i n a r y d e s i g n t o o l h a s b e e n d e v e l o p e d w i t h t h e a b i l i t y t o s i m u l t a n e o u s l y o p t i r i z e t h e p e r f o r m a n c e and n o i s e o f a p r o p e l - l e r . liy u s i n g a v o r t e x l a t t i c e a e r o d y n a m i c a n a l y s i s , a s u b s o n i c conipact s o u r c e n o i s e a n a l - y s i s , and a n o p t i m i z a t i o n scheme, a n e f f e c t i v e dnci f a s t p r e l i m i n a r y d e s i g n t o o l was c r e a t e d . T h i s p r o g r a m was t h e n u s e d t o i n v e s t i g a t e t h e n o i s e / p e r f o r m a n c e t r a d e - o f f s f o r a s t r a i g h t , a p r o p l e t e d , and a b i - b l a d e p r o p e l l e r .
W h i l e t h e r e s u l t s d e m o n s t r a t e t h e u t i l i t y o f s u c h a d e s i g n t o o l , more i m p o r t a n t l y , t h e r e l a t i v e m e r i t s o f t h e d i f f e r e n t n o i s e r e d u c t i o n t e c h n i q u e s a r e i d e n t i f i e d f o r o p t i n , i z e d geome- t r i e s . In s h o r t , f o r s t r a i g h t b l a d e s , i n c r e a s - i n g t h e b l a d e number w i l l i n c r e a s e e f f i c i e n c y a n d d e c r e a s e t h e n o i s e . Reducing t h e r o t a t i o n a l s p e e d w i l l a l s o r e d u c e t h e n o i s e h u t w i l l d e c r e a s e t h e e f f i c i e n c y s l i g h t l y . F o r a p r o - p l e t e d lade, t h e most f a v o r a b l e method i s t o r e d u c e t h e r o t a t i o n a l s p e e d , b u t a g a i n t h e r e i s a n e r f i c i e n c y p e n a l t y for n o i s e r e d u c t i o n .
F i n a l l y , f o r a h i - b l a d e p r o p e l l e r , e i t h e r a r o t a t i o n a l s p e e d r e a u c t i o n or s w e e p i n g t h e b l a d e w i l l r e d u c e n o i s e e f f e c t i v e l y . B u t , w i t h i t s i n i t i a l l y g r e a t e r e f f i c i e n c y , t h e r e i s a r e g i o n where t h e h i - b l a d e p r o p e l l e r h a s a h i g h e r e f f i - c i e n c y arid a l o w e r n o i s e l e v e l t h a n a s i m i l a r s t r a i g h t b l a d e p r o p e 1 l e r .
REFERENCES
1. L . K . Chang, and J . P . S u l l i v a n , " O p t i m i z a t i o n o f P r o p e l l e r B l a d e Shape by a n A n a l y t i c a l I ' l e thod ," A I A A P a p e r 82-1125, J u n e 1982.
2 . J . P . S u l l i v a n , L .K . Chang, and C . J . M i l l e r , "'The E f f e c t o f P r o p l e t s and R i - b l a d e s on t h e Pc,rformance and N o i s e of P r o p e l l e r s , " SAE P a p e r 810600, A p r i l 1981.
3. V . E . B a s k i n , L.S. V i l d g r u h e , Vozhdayev , Ye. S . , and G . I . Maykapar , "Theory o f t h e L i f t i n g A i r s c r e w , " NASA TT-F-823, F e b r u a r y 1 9 7 6 .
4 . L . J . B o b e r , and L . K . Chang, " F a c t o r s I n f l u e n c i n g t h e P r e d i c t e d P e r f o r m a n c e o f Advanced P r o p e l l e r D e s i g n s , " NASA TM-82676, 1 9 8 1 .
5. L . K . Chang, "The T h e o r e t i c a l P e r f o r m a n c e o f High E f f i c i e n c y P r o p e l l e r s , " Ph.D. T h e s i s , P u r d u e U n i v e r s i t y , 1980.
6. T .A . C g o l f , O . L . A n d e r s o n , D . E . Edwards , a n d A . J . L a n d g r e b e , "An A n a l y s i s f o r High Speed P r o p e l l e r - N a c e 1 l e Aerodynamic P e r f o r m a n c e P r e d i c t i o n . " Volume 1 , Theory and I n i t i a l A p p l i c a t i o n , NASA CR-169450, and Volume 2 , User ' s X a n u a l f o r t h e Computer Program, NASA CR-169451, (K79-912949-19, U n i t e d ' T e c h n o l o g i e s R e s e a r c h C e n t e r ; KASA C o n t r a c t NAS3-20961), J u n e 1979.
7. J . P . S u l l i v a n , "The E f f e c t o f B l a d e Sweep on P r o p e l l e r P e r f o r m a n c e , " AZAA P a p e r 77-716, J u n e 1977.
8. R . J . J e r a c k i , and G . A . f i t i t c h e l l , "Low and High Speed P r o p e l l e r s f o r G e n e r a l A v i a t i o n - P e r f o r m a n c e P o t e n t i a l and R e c e n t Wind T u n n e l T e s t R e s u l t s , " SAE P a p e r 811090, A p r i l 1981. N o t e : T h i s r e f e r e n c e d e s c r i b e s t h e t e s t s i n w h i c h t h e 0 . 5 6 6 s c a l e d a t a were o b t a i n e d . The d a t a c o n t a i n e d h e r e i n h a v e n o t y e t b e e n p u b l i s h e d and w e r e o b t a i n e d i n a p r i v a t e c o m m u n i c a t i o n w i t h R o b e r t J . J e r a c k i , P r o p e l l e r R e s e a r c h S e c t i o n , P r o p u l s i o n Aerodynamics D i v i s i o n , NASA L e w i s R e s e a r c h C e n t e r , C l e v e l a n d , O h i o , J a n u a r y 1983.
9 . G.P. S u c c i , D . H . Munro, J.A. Zimmer, P.D. Dunbeck , E . E . L a r a b e e , K . U . I n g a r d , and . J . L . K e r r e b r o c k , "Noise and P e r f o r m a n c e o f P r o p e l l e r s f o r L i g h t A i r c r a f t ," KASA CK-165732, 1981.
6
1 0 . M . V . Lowson, "The Sound F i e l d f o r S i n g u l a r i t i e s i n M o t i o n , " P r o c e e d i n g s o f t h e R o y a l S o c i e t y (London) , Vol . A286, 1 9 6 5 , pp . 559-572.
11. D . H . Munro, "The P r o d u c t i o n o f Sound b y Moving O b j e c t s , " Ph.D. T h e s i s , MIT, J u n e 1980.
1 2 . G.P. S u c c i , "Computed and E x p e r i m e n t a l P r e s s u r e S i g n a t u r e s f r o m Two 1 / 4 S c a l e G e n e r a l A v i a t i o n P r o p e l l e r s , " NASA CR-165 728, 1980.
1 3 . G.P. S u c c i , "Noise and P e r f o r m a n c e of G e n e r a l A v i a t i o n A i r c r a f t : A Review o f t h e MIT S t u d y , " SAE P a p e r 810586, A p r i l 1981.
1 4 . G.P. S u c c i , D . H . Munro, a n d J . A . Z i m m e r , " E x p e r i m e n t a l V e r i f i c a t i o n o f P r o p e l l e r N o i s e P r e d i c t i o n , " AIAA J o u r n a l , Vol . 2 0 , No. 11, November 1 9 8 2 , pp. 1483-1491.
1 5 . C . J . M i l l e r , " O p t i m a l l y D e s i g n e d P r o p e l l e r s C o n s t r a i n e d by N o i s e , " Ph.D. T h e s i s , P u r d u e U n i v e r s i t y , 1984.
1 6 . M . J . D . P o w e l l , "An E f f i c i e n t Method f o r F i n d i n g t h e Minimum o f a F u n c t i o n o f S e v e r a l V a r i a b l e s w i t h o u t C a l c u l a t i n g D e r i v a t i v e s , " Computer J o u r n a l , Vol . 7 , No. 2 , J u l y 1 9 6 4 , pp. 155-162.
1 7 . W . I . Z a n g w i l l , W . I . , "Minimiz ing a F u n c t i o n w i t h o u t C a l c u l a t i n g D e r i v a t i v e s , " Computer J o u r n a l , Vol . 1 0 , 1 9 6 7 , pp. 293-296.
18. A . V . F i a c c o , and G.P. McCormick, " N o n l i n e a r Programming," N e w York , J o h n W i l e y & Sons, 1968.
19 . S . G o l d s t e i n , "On t h e V o r t e x Theory o f S c r e w P r o p e l l e r s , " P r o c e e d i n g s of t h e R o y a l S o c i e t y o f London, S e r i e s A , Vol . 1 2 3 , 1 9 2 9 , pp. 440-465.
7
R &
0 NODE POINTS 0 CONTROL POINT
HELICAL HORSESHOE
STRENGTH r----
Figure 1. - L i f t ing l i n e geometry.
.25
.20
+ 0 . 15 +- m 3 CC I + s .10 + z w I=! LL LL
.05
0
-. 05 i
- A NASA TEST DATA, MACH = 0.11, B = 3 0 PREDICTION, p 3 / 4 = 28O, INVISCID 0 PREDICTION, p 3 / 4 = 28O, VISCOUS ESTIMATE
n A 32
.6 . 8 1.0 1.2 1.4 1.6 ADVANCE RATIO, J = V l n D
Figure 2. - Comparison of analyt ical and experimental t h r u s t coeff icients for t he LT10282+4 propeller. Experiniental data f ron, re ference [jl.
.25
.20
a 0
cf
0 a LL
+ z
- . 15
s 0 .10
w 0 8 .05 U U
0
0
NASA TEST DATA, M4CH = 0.11, B = 3 0 PREDICTION, B314 = 28O, INVISCID 0 PREDICTION, p 3 / 4 = 28O, VISCOUS ESTIMATE
- A
A
A a
a A 32
-. 05
ADVANCE RATIO, J = V i n D
F igu re 3. - Com2ar ison of ana ly t i ca l a n d exper imenta l power coef f i c ien ts fo r t h e LT10282+4 propel ler . Exper imenta l data f ro r r re fe rence @I.
.10
.08
k- 0 +- .06 Ln 3 C Y I t- LL
k- 0 . 0 4
0 - 5
0" .02 U LL
0
0
-. 02 0 .1 .2 . 3 . 4
ADVANCE RATIO, A = V / R R
F igu re 4. - Compar ison of ana ly t i ca l and exper imenta l t h r u s t coe f f i c ien ts fo r t h e 1C160 prope l le r . Exper i - men ta l data f r o m re fe rence [Q].
. 7
. 6
. 5
a 0
m- .4 s 0 a U
+ z w
0 . 3
0 u .2 5 L L
0
.1
0
-. 1 0
p
- 'RED ICTION
INVISCID
- \\ \ FnnMrln
J . 1 .2 . 3 . 4 ADVANCE RATIO, h = V / R R
Figure 5. - Comparison of analyt ical and experimental power coeff icients for t he 1C160 propeller. Experi- menta l data f r m reference [u] reduced in value by ha If.
I MASS SINKS:
Z
F igure 6. - Noise source locations.
PRED ICTIGN, VISCOUS -..
‘L THEORY
- EXPERIMENT
I -5 0 -1.5 -1. 0 -. 5 D . 5 1 .0 1.5
TIME, ms
F igu re 7. - A n a l y t i c a l a n d exper i r , en ta l compar ison of near - f ie ld no i se for prope l le r 1C160 in t h e p lane of rotation. Exper imenta l data a n d t h e o r y f ro l r l r e f e r - ences [&I, l a 5 1 .
m 8 1 r
.79 *801 BLADE NUMBER C 0 N S TAN T SOLIDITY \ BLADE NUM3ER C ON STA N T
SHIFT /
s 3
63 65 67 69 71 OASPL, dBA
.74
F igu re 8. - Opt imized n o i s e l p e r f o r m a n c e trade-of fs s t a r t i n g f ro r r t h e t h r e e way s t r a i g h t blade 6 3 ) base l ine con f igu ra t i on . Des ign po in t : J = 0.8, Cp = 0.154.
.79
.78
t 0 z W - 0 .77 U U W
.76
.75
s B3 .79 r
- R R E D U
-
-
-
.78
& .77 - 5 0 LL L L
.76
.75
.74
SPL, dBA
Figure 10. - Optimized noise lper formance trade-offs s tar t ing frorr, the th ree way syrnm?trical ly loaded bi-blade (SB3) baseline configuration. Design point ; J = 0. 8, Cp = 0.154.
0 R E D U -
-
-
-
LOADING SHIFT
1. Report No.
NASA TM-86967
Noise Constraints Effecting Optimal Propeller Designs
2. Government Accession No
7. Author(s)
Christopher J. Miller, Lewis Research Center, and John P. Sullivan, Purdue University, West Lafayette, Indiana
9. Performing Organization Name and Address
National Aeronautics and Space Administration Lewis Research Center Cleveland, Ohio 44135
2. Sponsoring Agency Name and Address
National Aeronautics and Space Administration Washington, D.C. 20546
Security Classif (of this report) 20 Security Classif (of this page) 21 No of pages
Unclassified Unclassified
3. Recipient's Catalog NO I
22 Price'
5. Report Date
~
6 Performing Organization Code
505-45-58 _____I
a P+rforrning Organizntror~ Report No
E-2449 Work Unit No.
_____- .____--
1 1 Contract or Grant No
13. Type of Report and Period Covered
Technical Memoranduiri ___- _..
14. Sponsoring Agency Code
FSupplementary Notes
Prepared for the SAE General Aviation Aircraft Meeting and Exposition sponsored by the Society of Automotive Engineers, Wichita, Kansas, April 16-19, 1985.
j. Abstract
A preliminary design tool for advanced propellers has been developed combining a fast vortex lattice aerodynamic analysis, a fast subsonic point source noise analysis, and an optimization scheme using a conjugate directions method. chord and sweep distributions are optimized to simultaneously improve both the aerodynamic performance and the noise observed at a fixed relative position. optimal noise/performance trade-offs for straight and advanced concept blades are presented. The techniques used include increasing the blade number, blade sweep, reducing the rotational speed, shifting the spanwise loading and diameter changes. Some methods yield improvement in both efficiency and noise.
Twist,
The
18. Distribution Statement Key Words (Suggested by Author@))
Performance; Aircraft; Aerodynamics; Blade; Optimization
Unclassified - unlimited STAR Category 02